The prion hypothesis poses a new paradigm for both infectivity and inheritance in which self- replicating alternate conformers of a normal, cellularly encoded protein specify new traits. In order for a protein to act in these roles, which have been historically limited to nucleic acids, a prion protein must traverse a multi-step pathway of changes in physical state and localization to ensure continued production of the alternate conformer and, thus, stability of the associated phenotype. A major challenge in prion biology is to understand the complex interplay between different conformers of the same protein in the same cell and the cellular regulation of this process. Given the dynamic nature of these interactions and the interdependency of the events in the multi-step prion cycle, development of a quantitative model that can be modified at any step would serve as a predictive tool in which experimental manipulations to the system could be designed and interpreted. Toward this end, I will develop a stochastic model of prion propagation in vivo and adapt this model to study two aspects of prion biology with direct implications for our understanding of human disease: the competition between prion conformers or strains, which has been linked to the interspecies transmission of prion diseases, and the mechanism by which mutations in the prion domain dominantly interfere with prion propagation by the wildtype protein, a process that will inform the rationale design of therapeutic targets. The combination of experimental tractability in the yeast system, which allows direct observations of protein conformation and activity in live cells, and the development of an accurate mathematical model provide a unique opportunity to meet these challenges.